It's not going to be a matter of punishment. This almost sets negotiation back to square one.
There are A LOT of effects in this that needs to be taken into account. Anything that's reciprocal currently (e.g. access to healthcare for Britons in Spain and for Spaniards in UK) is going to evaporate and will need to be reevaluated.
Now, the UK has clearly stated they don't like some things like free movement of people. The point of getting out of the EU is not to do a copy/paste of the current agreements and sign them in a week. The UK (not the EU) has decided to cancel everything and start from scratch because they don't feel like they could get to a comfortable situation inside the EU.
Even with the best of intentions, negotiating this kind of complex inter-state treaties take years. And, understandably, there will be extra care and friction because the UK has already got out once. Meanwhile, all the benefits are not going to be present.
I, sincerely, don't think we should think this in terms of "punishment", but if someone gets out of an agreement and immediately starts to renegotiate (more favourable) terms, it's reasonable to expect the negotiation to be hard...